question_answer

Suppose an electron is attracted towards the origin by a force \[\frac{k}{r}\] where 'k' is a constant and 'r' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be \['{{r}_{n}}'\] and the kinetic energy of the electron to be \['{{T}_{n}}'\]. Then which of the following is true?

A) \[{{T}_{n}}\propto \frac{1}{{{n}^{2}}},\,{{r}_{n}}\propto {{n}^{2}}\]

B) \[{{T}_{n}}\] independent of n, \[{{r}_{n}}\propto n\]

C) \[{{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto n\]

D) \[{{T}_{n}}\propto \frac{1}{n},\,{{r}_{n}}\propto {{n}^{2}}\]